In graph processing, a graph or network can have a set of vertices connected by a set of connectors. The connectors can have corresponding costs incurred associated with traversing the connection. The network can represent or be applied to many real-world conditions, for example, road networks, electronic circuitry, social media networks, computer networks, or the like. The determination of characteristics of the network, for example, the connectivity between two vertices and/or shortest path between two vertices, is desired. For networks with a large number of vertices and connectors, the determination of connectivity and the shortest paths between vertices is a time consuming problem and can require significant computing resources.